Optimal Geometric Factors
The first three terms of a geometric sequence are the integers $a$, $720$, and $b$, where ${a<720<b}$. What is the sum of the digits of the least possible value of $b$?
\[
\textbf{(A)}\ 9 \qquad
\textbf{(B)}\ 12 \qquad
\textbf{(C)}\ 16 \qquad
\textbf{(D)}\ 18 \qquad
\textbf{(E)}\ 21
\]